The answer linked in the commentary to your post is correct, faces cannot have holes within them, so each hole needs a minimum of two faces around it or put differently: a hole needs at least two connecting edges to surrounding geometry.
You say you have an object that "seems" to have a hole in the face. At first glance, without seeing more of the viewport I could not even tell if this is Wireframe mode or Solid and there simply are no faces, just edges.
But I suppose you have seen it in Solid mode and know there are faces. Did you go into Edit Mode? Are there really no connecting edges?
For Object Mode, there is a Wireframe setting in the Overlays. Behind the checkbox there is also a slider where you can change the value from 1 down to 0. All the way up to 1 it shows all edges in, decreasing the value lets edges disappear where the angle between the adjacent faces is below a certain threshold. The lower the value, the higher angled edges are hidden.
On a completely flat object, even the slightest bit lower than 1 makes all inner edges disappear, compare the left side with 1 to the right side with 0.999:
//EDIT: Regarding the additional information in your question: Sorry, but you did not create holes in faces without connecting edges. If you disable the Geometry Nodes modifiers and look at the base geometry in Edit Mode, there are lots of connecting edges around the hole:
You are not even using any kind of Mesh Boolean node inside the nodetree or any Boolean modifier outside and no Wireframe modifier either to achieve the result.
The only reason you don't have connecting edges in the "wire" is that you delete all geometry that you don't want to have a wire in the second Geometry Nodes modifier.
So if you would do something like that with the other object in your question instead of simply cutting holes with a Boolean modifier and throwing a Wireframe modifier on it afterwards, you could achieve the same result without connecting edges.